| 4π2 | (r – x) = | VE | , |
| T2 | r2 |
instead of what is in the text above; and this gives a slightly modified "third law." From this equation, if we have any distinct method of determining VE (and the next section gives such a method), we can calculate x and thus roughly weigh the moon, since
| r – x | = | E | , |
| r | E + M |
but to get anything like a reasonable result the data must be very precise.
No. 6. The force constraining the moon in her orbit is the same gravity as gives terrestrial bodies their weight and regulates the motion of projectiles.
Here we come to the Newtonian verification already several times mentioned; but because of its importance I will repeat it in other words. The hypothesis to be verified is that the force acting on the moon is the same kind of force as acts on bodies we can handle and weigh, and which gives them their weight. Now the weight of a mass m is commonly written mg, where g is the intensity of terrestrial gravity, a thing easily measured; being, indeed, numerically equal to twice the distance a stone drops in the first second of free fall. [See table [p. 205].] Hence, expressing that the weight of a body is due to gravity, and remembering that the centre of the earth's attraction is distant from us by one earth's radius (R), we can write
| mg = | VmE | , |
| R2 |
or
VE = gR2 = 95,522 cubic miles-per-second per second.